Carry out Maria Agnesi's proof of the Quotient Rule from her...

Carry out Maria Agnesi's proof of the Quotient Rule from her book
on calculus, published in $178 :$ Assume that $f, g$ and $h=f / g$ are differentiable. Compute the derivative of $h g=f$ using the Product Rule,
and solve for $h^{\prime} .$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Differentiability

This concept refers to the property of a function having a derivative at every point in its domain. Differentiability is a fundamental requirement in calculus for applying laws of differentiation, ensuring that operations like the product and quotient rules can be validly executed.

Product Rule

The product rule is a fundamental principle in differential calculus which states that the derivative of a product of two differentiable functions is given by the derivative of the first function times the second function plus the first function times the derivative of the second function. It is a crucial tool for finding derivatives when functions are multiplied together.

Quotient Rule

The quotient rule is a method for differentiating a function that is the quotient of two differentiable functions. It is derived by expressing the quotient as a product of the numerator and the reciprocal of the denominator, and then applying the product rule along with the chain rule. The derivation typically involves differentiating an equivalent form of the quotient and then solving for the derivative of the original quotient function.

Transcript

Please give Ace some feedback